= Solution
Assume $\dim(N)=|N|=\kappa$, with $\kappa\geq|L|+\aleph_0$. Let $A\subseteq N$ have size below $\kappa$ and let $p(x)\in S_1(A)$ be a <complete type>. If $p$ is algebraic, its realizations lie in $\operatorname{acl}(A)\subseteq\operatorname{acl}(N)=N$. If $p$ is nonalgebraic, strong minimality makes it the unique generic type over $\operatorname{acl}(A)$. The <pregeometry> exchange property gives
$$
\dim\operatorname{acl}(A)\leq|A|<\kappa=\dim(N),
$$
so some basis element of $N$ lies outside $\operatorname{acl}(A)$ and realizes $p$.
Thus $N$ realizes every one-type over every parameter set of size below $\kappa$. The standard one-type characterization, applied successively to tuple coordinates, makes $N$ $\kappa$-saturated. Consequently
$$
\boxed{\dim(N)=|N|\Longrightarrow N\text{ saturated}.}
$$
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